Various techniques may be used to evaluate geological formations. For example, measurements may be made using tools located within a borehole such as in support of geophysical and petrophysical exploration or resource extraction. In one approach, an acoustic or “sonic” logging technique is used. An acoustically transmitting transducer is located in the borehole and is electrically driven to insonify a region nearby the transducer. Insonification induces propagating acoustic waves in the borehole, within the geologic formation through which the borehole extends, or along the interface between the geologic formation and the borehole. An acoustic receiving section then detects reflected or refracted acoustic energy, such as using receive transducers at locations spaced apart from the acoustic transmitter.
In one approach, a monopole acoustic transducer is used for transmitting or receiving. In a transmission application, the monopole acoustic transducer generally emits an acoustic wavefront having spherical or cylindrical uniformity. Such a symmetric wavefront induces a compressive wavefront or “P-wave.” A portion of the P-wave is reflected by the interface between the borehole and the formation at the borehole wall, and a portion of the P-wave is refracted within the formation. As the propagation direction of the refracted portion of the P-wave converges on the borehole-formation interface, a portion of the refracted P-wave energy is transferred back into the borehole (e.g., a first “head wave”). Reflected or refracted waves are then detected at respective locations remotely with respect to the transmitting transducer, such as a few meters or tens of meters away, providing information about the propagation characteristics of the formation (and thus information indicative of formation composition or porosity). A time difference between arrivals of the P-waves at respective transducers is divided by a distance between the transducers to obtain a “slowness” parameter, having units that represent an inverse of velocity (e.g., microseconds per foot or microseconds per meter).
A transverse or shear wavefront, referred to as an “S-wave,” may also be induced in the formation by a monopole transducer, if the formation supports a shear wave speed faster than the velocity of a wave traveling exclusively in the fluid surrounding the borehole (e.g., a “mud wave”). When this condition is met, the formation is referred to as a “fast formation.” The S-wave is similarly refracted toward the borehole-formation interface, and is detected at the respective remote locations typically following the refracted P-wave. In this manner, “shear slowness” is then determined using the time difference between arrivals of a shear wave signature at respective receiving transducers, divided by the distance between the transducers.
Other acoustic propagation modes are also supported, such as a surface wave at the borehole-formation interface, referred to as a “Stoneley wave.” The arrival of the Stoneley wave at the receiving transducers generally occurs after the refracted P-wave and S-wave arrivals, and the Stoneley wave exhibits a varying degree of penetration into the formation and a slightly varying propagation velocity depending on the frequency of acoustic energy. Information about such frequency dependence or “dispersion” is used to provide information about formation permeability.
In some approaches, a dipole acoustic transducer structure may be used to provide acoustic energy to excite the formation or to receive acoustic energy coupled from the formation to the transducer structure through the borehole. A dipole acoustic transducer provides the ability to excite shear waves in formations where a shear wave propagation velocity is lower than a borehole propagation velocity, a configuration referred to as a “slow” formation. Unlike a monopole transducer, a dipole transducer can excite a dispersive flexural mode in a “slow” formation which propagates at a velocity corresponding to a shear wave velocity in the low frequency range.
A presence of the acoustic logging tool in the borehole environment alters the acoustic propagation environment within the borehole. Acoustic waves propagating within or along the acoustic logging tool body encounter an acoustic frequency-dependent or dispersive effect. Failure to account for the dispersion contribution of the acoustic logging tool on the borehole propagation environment may compromise the accuracy of other operations involving determination of geologic formation properties, particularly for measurements involving flexural waves such as shear waves.